Dear John,
Thank you for the link, I read it, I also read one of the papers in the references, however I still, dont see a physical prove of the "phenomenon".
Best regards
Hi,
The question is incorrect. Let's see...
The use of the word "particle" in this context is wrong as there is nothing of the sort independent of what we want to know. In fact there is nothing before we measure something as Bell's inequalities prove quantum mechanics which is true experimentally is incompatible with a measurement -preexisting physical reality. Locality which is often synonymous of "particle" is a classical property due to a decoherence of quantum superpositions observed at our human scale of things, but fundamentally nothing is local. Therefore there is no "particle" here or there before you look through your instruments to see if it is. Now, when you do a measurement to know the position of a free particle you collapse the superposition of all the states where the property "position" takes a specific value an "Eigen value" in each state to a subset of the Hilbert space, a vector space generated by the states |X> for X in the interval ]X-x,X+x[ where 2x is the precision of the measurement and may be made arbitrarily small compared to X but not zero since the probability of "X equal some X0" is zero since X is a continuous variable. Measuring the property "position" at the same time around two locations in space means that you are collapsing the superposition of states to two disjoint subsets of the Hilbert space say, |X> in [X1-x,X1+x]U[X2-x,X2+x] thus the new state of the system is a linear superposition of all these states in this sense only we can say that the property "position" of the system takes simultaneously all these Eigen values as we could say it from the beginning for the superposition of all the states |X> where X ]-inf,inf[.
Hi Faical,
Thank you for the answer,
Maybe I wasn't very specific in my question therefor I will try to use examples and be more specific, by asking these questions :
1. Is an electron a particle (i.e is it bounded in space ?).
2. If it is indeed bounded in space and have a rest mass, can IT exist in two different places (bounded regions ) at the same time, -hypothetically without doing any measurements-.
3. you wrote "fundamentally nothing is local " Is that something that we proved in a lab or we take it as a hypotheses ?
And finally to make it easier for me to SEE, whether what we are talking about here is a physical FACT, meaning something that we go to the lab with instruments and do measurements and TRY to interpret these measurements, or it is just an attempt to MODEL mathematically what we think is going on, and everyone can say whatever they want, as long as it doesn't go against the measured data that we have, I will ask this question
When you wrote " Now, when you do a measurement to know the position of a free particle you collapse the super ...." Is that something you do in a Lab, and did you do it ? if yes what exactly did you do ? or it is a mathematical model ?
Thank you in advance, and I hope you didn't feel attacked by these questions, my objective if to have evidence in what I say.
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